Next: Differential dilation matrix elements:
Up: Other matrix elements
Previous: Momentum matrix elements:
For we have for each component
of the dipole (position) operator,
where as before
This follows from row 3 of the matrix
Summation over is implied. A mixture of vector and Einstein notations has
In the Dirichlet BC case this becomes
Note that the integral is proportional to the matrix element
of the billiard deformation corresponding to translation in the direction.
No form for has been found.
The corresponding unit vector
does not lie in
the row space of
, indicating that other boundary
derivatives are needed as input.